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arXiv · 2412.07361

Optimizing quasi-dissipative evolution equations with the moment-SOS hierarchy

Saroj Prasad Chhatoi·Didier Henrion·Swann Marx·Nicolas Seguin
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Abstract

We prove that there is no relaxation gap between a quasi-dissipative nonlinear evolution equation in a Hilbert space and its linear Liouville equation reformulation on probability measures. In other words, strong and generalized solutions of such equations are unique in the class of measure-valued solutions. As a major consequence, non-convex numerical optimization over these non-linear partial differential equations can be carried out with the infinite-dimensional moment-SOS hierarchy with global convergence guarantees. This covers in particular all reaction-diffusion equations with polynomial nonlinearity.

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Saroj Prasad Chhatoi, Didier Henrion, Swann Marx, Nicolas Seguin. 2025-07-07. Optimizing quasi-dissipative evolution equations with the moment-SOS hierarchy. https://arxiv.org/abs/2412.07361

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